Simplify the following expression: $ z = \dfrac{-7}{8} - \dfrac{-5n - 2}{-10n + 2} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10n + 2}{-10n + 2}$ $ \dfrac{-7}{8} \times \dfrac{-10n + 2}{-10n + 2} = \dfrac{70n - 14}{-80n + 16} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-5n - 2}{-10n + 2} \times \dfrac{8}{8} = \dfrac{-40n - 16}{-80n + 16} $ Therefore $ z = \dfrac{70n - 14}{-80n + 16} - \dfrac{-40n - 16}{-80n + 16} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{70n - 14 - (-40n - 16) }{-80n + 16} $ Distribute the negative sign: $z = \dfrac{70n - 14 + 40n + 16}{-80n + 16}$ $z = \dfrac{110n + 2}{-80n + 16}$ Simplify the expression by dividing the numerator and denominator by -2: $z = \dfrac{-55n - 1}{40n - 8}$